Vesko Valov

Continuous selections and -spaces

A characterization of paracompact C-spaces via continuous selections avoiding Z∞-sets is given. The result is applied to prove a countable sum theorem for paracompact C-spaces, and to obtain a new partial solution of a question raised by E. Michael.

Dense Families of Selections and Finite-Dimensional Spaces

A characterization of n-dimensional spaces via continuous selections avoiding Zn-sets is given, and a selection theorem for strongly countable-dimensional spaces is established. We apply these results to prove a generalized Ostrands theorem, and to obtain a new alternative proof of the Hurewicz formula. It is also shown that our selection theorem yields an easy proof of a Michaels result.

The Extension Dimension and C-Spaces

Some generalizations of the classical Hurewicz formula are obtained for extension dimension and C-spaces. A characterization of the class of metrizable spaces which are absolute neighborhood extensors for all metrizable C-spaces is also given.

ON FINITE-DIMENSIONAL MAPS II

Abstract Let f :X→Y be a perfect n-dimensional surjective map of paracompact spaces and Y a C-space. We consider the following property of continuous maps g :X→ I k =[0,1] k , where 1⩽k⩽ω: each g(f−1(y)), y∈Y, is at most n-dimensional. It is shown that all maps g∈C(X, I n+1 ) with the above property form a dense Gδ-set in the function space C(X, I n+1 ) equipped with the source limitation topology. Moreover, for every n+1⩽m⩽ω the space C(X, I m ) contains a dense Gδ-set of maps having this property.

Cantor set selectors

Abstract If every l.s.c. mapping from the Cantor set C to the closed subsets of a metric space X admits a u.s.c. selection, then X is a Baire space and either X is scattered or X contains a copy of C .

Universal absolute extensors in extension theory

Let L be a countable and locally finite CW complex. Suppose that the class of all metrizable compacta of extension dimension ≤ (L) contains a universal element which is an absolute extensor in dimension (L). Our main result shows that L is quasi- finite.

Parametric Bing and Krasinkiewicz maps: revisited

Let

Topology in North Bay: Some problems in continuum theory, dimension theory and selections

M

Alexandroff Manifolds and Homogeneous Continua

be a complete metric

Skeletally Dugundji spaces

ANR